He said police have since charged two teenage girls, aged 13 and 14, with aggravated robbery.
The pair will appear in the Auckland Youth Court.
"We want to assure our community that we are treating this matter very seriously and are continuing to follow positive lines of inquiry to identify and locate the other four people involved," Cox said.
"This was a very traumatic experience for the victims and we remain in close contact with them."
Kiwi Indian Association organiser Sunny Kaushal spoke to the Herald after returning from North Shore Hospital where one of the shopkeepers was awaiting further surgery.
"He is so badly beaten, his right arm is - oh my gosh," he said.
"His muscles are almost dead."
He said the shopkeeper's wife was also injured during the incident and suffered "lots of bruises".
She has since been discharged from hospital.
Tonight, a meeting for local shopkeepers will be held to show solidarity for the couple and discuss a perceived rise in violence against store attendants.
Inspector Jacqui Whittaker, the Area Commander for the Auckland City western area, also attended the meeting.
Yesterday, a police car was fired upon during a chase through South Auckland after an armed robbery at a dairy.
Inspector Dave Glossop, of Counties Manukau Police, said police were called to the store in Mangere about 2pm after reports of two men entering the shop and firing a gun.
"There were four staff members in the dairy at the time as well as members of the public, including children," Glossop said.
"[The offenders] have fled the scene allegedly taking the store's till and getting into a waiting vehicle."
He said police pursued the vehicle but abandoned the pursuit after a shot was fired at the police car.
With help from the police Eagle Helicopter and the public, three men, aged 29, 26 and 21 were later arrested.
A firearm was also recovered, Glossop said.
"The victims are obviously shaken by what has occurred and are being supported by victim support and police.
"This was a very serious incident and we are relieved that no one was injured."
On Sunday, a service station in Auckland's northwest was also held up and the attendant threatened with a knife.
Three men who had their faces covered stormed the BP in Kumeu on State Highway 16 about 5.50am, stealing cash and cigarettes.
